Few newer games will even work well with 256MB memory with a real video card, let alone with an integrated card that steals 64Megs from the system RAM. When that integrated solution is on the old side and slow even for integrated video? Umm yeah, not much. Maybe UT2004 with the options WAY down, or in software rendering mode, but then your CPU and lack of RAM due to the integrated video becomes an issue.
You're going to have to stick with older games.
If you have an AGP slot, et on eBay and pick something up for like $30. 64 megs. Geforce 2 (not MX), Geforce3, or a RAdeon 8500LE. I'd try to swing a GF3-ish or 8500LE if you can. It's VERY low budget and not the ideal solution, but it will work.
I have my girlfriend's little brother set up with an Athlon 900 and a GeForce2, he can play Morrowind and BF1942 okay. I think he played NFS:U alright with it too.